How do you find the accelerations?

Question

I'm having trouble figuring out the answer to the problem on

http://www.mathparadise.com/?p=39

Shouldn't the acceleration be the same?

Answer 1

That picture doesn't make much sense. Maybe the picture is incomplete; check with your professors. Maybe its trying to indicate that the pulley system on the left has the 10 pound mass in free fall??? If this is the case, then the magnitutde of the acceleration on the pulley system on the right is obviously greater than that on the left, since on the right, there is a net force of 40 lb pulling upward on the 10 pound mass; and on the left, there is a net force of 10 lb (from gravity) pulling the mass down.

The main thing is to know how to calculate the accelerations using Newton's Laws. Are the pulleys massless? If not, you will have to integrate the concept of torque and rotational dynamics into the problem to.

Hope this explanation helps.  

Answer 2

T2 will always be 50 lb but T1 will be 50 lb minus m*a, the force to accelerate the 50 lb mass.

Ergo, situation 2 will accelerate more rapidly.